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Bunuel
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What percentage of families in the state have annual incomes over $50 09 Jul 2015, 03:56
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C
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35% (medium)

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68% (01:16) correct 32% (01:09) wrong based on 353 sessions

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What percentage of families in the state have annual incomes over $50,000 and have a net worth over $500,000?

(1) 65% of all the families in the state have an annual income over $50,000.
(2) 20% of the families in the state with an annual income over $50,000 have a net worth above $500,000.

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C
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What percentage of families in the state have annual incomes over $50 09 Jul 2015, 04:19
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Bunuel
What percentage of families in the state have annual incomes over $50,000 and have a net worth over $500,000?

(1) 65% of all the families in the state have an annual income over $50,000.
(2) 20% of the families in the state with an annual income over $50,000 have a net worth above $500,000.

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These questions are best solved by using the Double Matrix or venn-Diagram so here are both. [I suggest and prefer Double Matrix over Venn-Diagram in case of two set Questions]

Answer: Option C
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What percentage of families in the state have annual incomes over $50 09 Jul 2015, 06:21
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Bunuel
What percentage of families in the state have annual incomes over $50,000 and have a net worth over $500,000?

(1) 65% of all the families in the state have an annual income over $50,000.
(2) 20% of the families in the state with an annual income over $50,000 have a net worth above $500,000.

Kudos for a correct solution.
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Bunuel: the title of the topic does not pertain to the actual question.

As for the question, refer to the attached image for the solution.

AI: Families with annual income >50,000
NAI: fFamilies with annual income <50,000

NW: families with net worth >500,000
NNW: families with net worth <500,000

need to find = X (in the attached figure)

As this is a percentage question, assume total families =100 and follow the solution in the attached image.

Statement 1, provides us the information about families that have annual income > 50,000. This does not help in finding the percentage of families out of these 65% who also have net worth > 50000. Thus this statement is not sufficient.

Statement 2, Tells us that X=0.2Y (in the attached figure) but we do not have another equation to solve for both x and y. Thus this statement is not sufficient.

Combining, we see X=0.2Y and Y =65. Thus value of X can be found. ----> C is the correct answer.

C is the correct answer.
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What percentage of families in the state have annual incomes over $50 13 Jul 2015, 03:03
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Bunuel
What percentage of families in the state have annual incomes over $50,000 and have a net worth over $500,000?

(1) 65% of all the families in the state have an annual income over $50,000.
(2) 20% of the families in the state with an annual income over $50,000 have a net worth above $500,000.

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800score Official Solution:

(C) Statement (1) alone is not sufficient, because it only gives us the percentage of families in the state with the required annual income, but gives no information regarding the net worth.

Statement (2) is not sufficient because, although it tells you about the percentage of families that satisfy the question, it does not give you the percentage of families in the state that have an annual income of $50,000.

Statements (1) and (2) COMBINED are sufficient. 20% of the 65% are families who both have annual incomes over $50,000 AND have a net worth above $500,000. To find out the percentage of people with both traits, multiply the two independent variables. The two statements give these two variables.

Remember, however, that for these questions you do not need to solve for an answer; you simply need to establish whether or not you have sufficient information to do so.
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What percentage of families in the state have annual incomes over $50 10 Oct 2024, 03:57
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High networthLow net worth
high incomeab
low incomecd
total


we want \frac{a}{tot}

(1) a+b = 65% tot
NS

High networthLow net worth
high incomeab65% tot
low incomecd35% tot
total


(2) 20% of the families in the state with an annual income over $50,000--> 20%(a+b) have a net worth above $500,000 = a
High networthLow net worth
high income20%(a+b)a+b
low incomecd
total

20%(a+b) = a
0.2a + 0.2b = a
0.2b = 0.8a

b = 4a

a = 4/5 (a+b)
NS

(1)(2)
High networthLow net worth
high income20%(a+b)80%(a+b)65%(a+b)
low incomecd
total

a+b = 65% tot
a = 4/5 (a+b)

we can solve and find a

a5/4 = (a+b) = 65% tot
a5/4 = 65% tot
a = 65% 4/5 tot =0.52 tot Sufficient
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